MinT - Best Known (99, 190, s)-Nets in Base 4

Best Known (99, 190, s)-Nets in Base 4

(99, 190, 104)-Net over F₄ — Constructive and digital

Digital (99, 190, 104)-net over F₄, using

t-expansion [i] based on digital (73, 190, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(99, 190, 158)-Net over F₄ — Digital

Digital (99, 190, 158)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 190, 1948)-Net in Base 4 — Upper bound on s

There is no (99, 190, 1949)-net in base 4, because

1 times m-reduction [i] would yield (99, 189, 1949)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 629705 969116 938208 717569 549534 149321 189506 191809 699517 428884 183850 305220 754830 580465 872175 371286 017247 086317 508560 > 4¹⁸⁹ [i]